Lines and Angles Class 6 Worksheet — Free PDF Download with Answers

Lines and angles are the building blocks of geometry. A line extends infinitely in both directions and has no endpoints, while a line segment has two endpoints and a fixed length. A ray has one endpoint and extends infinitely in one direction. When two rays share a common starting point, they form an angle.

In Class 6, students learn to identify these geometric objects, classify angles by their measure, and understand relationships between angles such as complementary and supplementary pairs. This chapter lays the groundwork for everything from triangle properties in Class 7 to coordinate geometry in Class 10.

Beyond the classroom, angles are everywhere — in architecture, engineering, sports, and even art. Understanding how to measure and classify angles gives students a vocabulary for describing the physical world precisely.

Core ideas to revise before the worksheet:

* Point — A location in space with no size. Denoted by a capital letter (e.g., $A$).
* Line — Infinite in both directions, denoted $\overleftrightarrow{AB}$.
* Line segment — Finite, denoted $\overline{AB}$, with a measurable length.
* Ray — One endpoint, extends infinitely, denoted $\overrightarrow{AB}$ (starts at $A$).
* Angle — Formed by two rays with a common vertex. Measured in degrees ($^\circ$).
* Types of angles:
- Acute: $0^\circ < \theta < 90^\circ$
- Right: $\theta = 90^\circ$
- Obtuse: $90^\circ < \theta < 180^\circ$
- Straight: $\theta = 180^\circ$
- Reflex: $180^\circ < \theta < 360^\circ$
* Complementary angles — Two angles whose sum is $90^\circ$.
* Supplementary angles — Two angles whose sum is $180^\circ$.
* Perpendicular lines — Two lines meeting at $90^\circ$.
* Parallel lines — Two lines in the same plane that never meet.

1. Print the PDF — Download using the links below. Keep a protractor, ruler, and pencil handy.

2. Start with Level 1 (Easy) — 20 questions on identifying lines, rays, segments, and classifying angles. Aim for near-perfect accuracy.

3. Time yourself — 15 minutes for Level 1, 20 for Level 2, 25 for Level 3.

4. Check answers — Use the included answer key.

5. Revise mistakes — Redraw the figure for every wrong answer and label each element correctly.

6. Move to the next level — Progress when you score 16/20 or above.

Level 1 — Easy

1. Classify the angle: $\angle P = 72^\circ$.
Solution: $0^\circ < 72^\circ < 90^\circ$, so it is an acute angle.

2. Name the line segment joining points $M$ and $N$.
Solution: $\overline{MN}$.

3. Two angles are supplementary. One is $110^\circ$. Find the other.
Solution: $180^\circ - 110^\circ = 70^\circ$.

Level 2 — Medium

1. The complement of an angle is $18^\circ$ more than the angle itself. Find the angle.
Solution: Let the angle be $x$. Then $x + (x + 18) = 90 \Rightarrow 2x = 72 \Rightarrow x = 36^\circ$.

2. Two lines intersect at point $O$. If one of the angles formed is $65^\circ$, find all four angles.
Solution: Vertically opposite angles are equal: $65^\circ, 115^\circ, 65^\circ, 115^\circ$.

3. Is it possible for two obtuse angles to be supplementary? Why?
Solution: No. Each obtuse angle is $> 90^\circ$, so their sum would exceed $180^\circ$.

Level 3 — Hard

1. Three lines meet at a point forming six angles. If two adjacent angles are $55^\circ$ and $40^\circ$, find all six angles.
Solution: The third angle adjacent to these two is $360^\circ - 2(55 + 40 + \text{third})$. Actually, three lines at a point create 6 angles. Opposite angles are equal. Third pair angle $= 180^\circ - 55^\circ - 40^\circ = 85^\circ$. Six angles: $55^\circ, 40^\circ, 85^\circ, 55^\circ, 40^\circ, 85^\circ$.

2. An angle is $\frac{1}{3}$ of its supplement. Find the angle.
Solution: Let angle $= x$. Supplement $= 180 - x$. Given $x = \frac{1}{3}(180 - x) \Rightarrow 3x = 180 - x \Rightarrow 4x = 180 \Rightarrow x = 45^\circ$.

3. In the figure, $\overrightarrow{OA}$ and $\overrightarrow{OB}$ are opposite rays. $\overrightarrow{OC}$ makes $\angle AOC = 3x + 10$ and $\angle BOC = 2x + 20$. Find $x$.
Solution: Since $\overrightarrow{OA}$ and $\overrightarrow{OB}$ are opposite rays, $\angle AOC + \angle BOC = 180^\circ$. So $3x + 10 + 2x + 20 = 180 \Rightarrow 5x = 150 \Rightarrow x = 30$.

CBSE (NCERT — Ganita Prakash / Math Magic)
The "Lines and Angles" chapter covers basic definitions, angle measurement with a protractor, and classification. CBSE emphasises hands-on activities like paper-folding to discover right angles and supplementary pairs. The Ganita Prakash textbook adds exploratory tasks.

ICSE (Selina / ML Aggarwal)
ICSE covers this under "Basic Geometry" or "Basic Geometrical Concepts." The treatment is similar but includes more construction-based questions (using compass and straightedge). ICSE exams often include numerical problems on complementary/supplementary angles alongside diagram-based identification.

IB MYP (Mathematics Framework)
The MYP "Geometry Basics" unit takes an investigative approach. Students explore angle relationships through real-world contexts (architecture, design) and are expected to justify their answers in writing. The focus is on reasoning rather than rote classification.

Key Differences:
* CBSE: Activity-based learning; protractor usage tested.
* ICSE: Construction questions included; more numerical problems.
* IB: Investigative and justification-oriented.

Download your free Lines and Angles worksheets:

* Lines and Angles CBSE Worksheet — 60 questions aligned to NCERT
* Basic Geometry ICSE Worksheet — 60 questions aligned to Selina / ML Aggarwal

Practise online with instant feedback:

* Practice Online — CBSE
* Practice Online — ICSE
* Practice Online — IB

Each worksheet has 20 questions per level with a detailed answer key.

* AI Maths Solver — Upload a geometry diagram and get a step-by-step solution.
* Spark Coach — AI tutor that guides without giving away answers.
* Free Worksheets for All Classes — Browse Class 1-10 worksheets across CBSE, ICSE, and IB.
* Play Mode for Class 1-4 — Fun geometry games for younger learners.

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